Group delay estimate system using least square fit to phase response ramp

Abstract

The phase response of a network is measured at uniform frequency intervals. A linear regression analysis is performed on samples of the phase response measured at frequencies within an aperture centered on a group delay frequency to obtain an estimate of the group delay of the network at that frequency. The process is repeated for a sequence of group delay frequencies to determine a trace of the group delay of the network across a range of frequencies.

I claim: 
     
       1. In an electronic measurement instrument, a method for estimating a trace of second measurements related to the derivative of a trace of first measurements of an electrical property of a network, the method comprising: obtaining a plurality of uniformly spaced samples of a first measurement to form the first trace; and   performing a least mean squares fit to samples in the first trace within each of a plurality of apertures to determine a plurality of estimates of a second measurement for forming the second trace.   
     
     
       2. The method of claim 1 further comprising multiplying the second trace by a constant multiplier to form a trace of estimates of the second measurement. 
     
     
       3. The method of claim 2 wherein the first measurements are the phase response of a network sampled at uniformly spaced frequencies and the second measurements are the group delay of the network at various frequencies. 
     
     
       4. The method of claim 1 wherein the first measurements are the phase of a signal sampled at uniformly spaced sample times and the second measurements are the instantaneous frequency of the signal at various times. 
     
     
       5. The method of claim 1 comprising: determining a first estimate in the second trace by performing a least mean square error fit to samples of the first trace within a first aperture;   determining each subsequent estimate in the second trace by determining a value which, when added to a previous estimate adjacent the subsequent estimate, provides a least mean square error fit to samples of the first trace within a subsequent aperture of the plurality of apertures, and adding the value to the previous estimate to form the subsequent estimate.   
     
     
       6. An electronic measurement instrument comprising: a reference receiver connectable to an input of a network to receive a stimulus signal;   a response receiver connectable to an output of the network to receive a network output signal produced by the network in response to the stimulus signal;   means for measuring the phase response of the network at uniform intervals of frequency; and   means for performing a least mean squared error analysis on a number of phase response measurements made at frequencies within each of a plurality of apertures to estimate a group delay trace of the network at a plurality of selected frequencies.   
     
     
       7. The instrument of claim 6 wherein the means for measuring the phase response of the network is a phase response processor for determining an array of phase response data measured at uniform frequency intervals from samples of the stimulus signal and the network output signal. 
     
     
       8. The instrument of claim 7 wherein the means for performing the least mean square error analysis is a group delay processor for performing the least mean squared error analysis on subsets of the array to yield estimates of the group delay of the network at a plurality of selected frequencies. 
     
     
       9. The instrument of claim 6 wherein the means for measuring the phase response and the means for performing the least mean square error analysis are embodied in a single processor. 
     
     
       10. The instrument of claim 6 wherein the phase response measurements are measurements of the cumulative phase response of the network. 
     
     
       11. The instrument of claim 6 wherein the phase response measurements are measurements of the difference in phase response of the network between two adjacent frequencies. 
     
     
       12. The method of claim 3 comprising: determining a first estimate in the second trace by performing a least mean square error fit to samples of the first trace within a first aperture;   determining each subsequent estimate in the second trace by determining a value which, when added to a previous estimate adjacent the subsequent estimate, provides a least mean square error fit to samples of the first trace within a subsequent aperture of the plurality of apertures, and adding the value to the previous estimate to form the subsequent estimate.   
     
     
       13. The method of claim 3 further comprising multiplying the second trace by a constant multiplier to form a trace of estimates of the second measurement. 
     
     
       14. The method of claim 4 comprising: determining a first estimate in the second trace by performing a least mean square error fit to samples of the first trace within a first aperture;   determining each subsequent estimate in the second trace by determining a value which, when added to a previous estimate adjacent the subsequent estimate, provides a least mean square error fit to samples of the first trace within a subsequent aperture of the plurality of apertures, and adding the value to the previous estimate to form the subsequent estimate.   
     
     
       15. The method of claim 4 further comprising multiplying the second trace by a constant multiplier to form a trace of estimates of the second measurement. 
     
     
       16. In an electronic measurement instrument, a method for estimating a trace of second measurements related to the derivative of a trace of first measurements of an electrical property of a network, the method comprising: obtaining a plurality of uniformly spaced samples of a first measurement to form the first trace; and   performing a least mean squares fit of a linear function to samples in the first trace within each of a plurality of apertures, wherein at least two of the apertures have more than one of the samples in common; and   determining a plurality of estimates of a second measurement centered in the apertures to form the second trace.   
     
     
       17. The method of claim 16 further comprising multiplying the second trace by a constant multiplier to form a trace of estimates of the second measurement. 
     
     
       18. The method of claim 16 wherein the first measurements are the phase response of a network sampled at uniformly spaced frequencies and the second measurements are the group delay of the network at various frequencies. 
     
     
       19. The method of claim 16 wherein the first measurements are the phase of a signal sampled at uniformly spaced times and the second measurements are the instantaneous frequency of the signal at various times. 
     
     
       20. The method of claim 16 comprising: determining a first estimate in the second trace by performing a least mean square error fit to samples of the first trace within a first aperture;   determining each subsequent estimate in the second trace by determining a value which, when added to a previous estimate adjacent the subsequent estimate, provides a least mean square error fit to samples of the first trace within a subsequent aperture of the plurality of apertures, and adding the value to the previous estimate to form the subsequent estimate.